Sys.Date()

## [1] "2020-12-18"

Authors: Hanna Klimczak, Kamil Pluciński

Libraries used

library(plotly)
library(knitr)
library(kableExtra)
library(caret)

Providing data reproductibility

To ensure that running the notebook will always return the same output, we set seed to 0.

set.seed(0)

Reading data from file

data <- read.csv("Life_Expectancy_Data.csv")
kable(head(data), "html") %>% kable_styling("striped") %>% scroll_box(width = "100%")

Country	Year	Status	Life.expectancy	Adult.Mortality	infant.deaths	Alcohol	percentage.expenditure	Hepatitis.B	Measles	BMI	under.five.deaths	Polio	Total.expenditure	Diphtheria	HIV.AIDS	GDP	Population	thinness..1.19.years	thinness.5.9.years	Income.composition.of.resources	Schooling
Afghanistan	2015	Developing	65.0	263	62	0.01	71.279624	65	1154	19.1	83	6	8.16	65	0.1	584.25921	33736494	17.2	17.3	0.479	10.1
Afghanistan	2014	Developing	59.9	271	64	0.01	73.523582	62	492	18.6	86	58	8.18	62	0.1	612.69651	327582	17.5	17.5	0.476	10.0
Afghanistan	2013	Developing	59.9	268	66	0.01	73.219243	64	430	18.1	89	62	8.13	64	0.1	631.74498	31731688	17.7	17.7	0.470	9.9
Afghanistan	2012	Developing	59.5	272	69	0.01	78.184215	67	2787	17.6	93	67	8.52	67	0.1	669.95900	3696958	17.9	18.0	0.463	9.8
Afghanistan	2011	Developing	59.2	275	71	0.01	7.097109	68	3013	17.2	97	68	7.87	68	0.1	63.53723	2978599	18.2	18.2	0.454	9.5
Afghanistan	2010	Developing	58.8	279	74	0.01	79.679367	66	1989	16.7	102	66	9.20	66	0.1	553.32894	2883167	18.4	18.4	0.448	9.2

Dataset summary and basic statistics

nrow(data)

## [1] 2938

kable(summary(data), "html") %>% kable_styling("striped") %>% scroll_box(width = "100%")

	Country	Year	Status	Life.expectancy	Adult.Mortality	infant.deaths	Alcohol	percentage.expenditure	Hepatitis.B	Measles	BMI	under.five.deaths	Polio	Total.expenditure	Diphtheria	HIV.AIDS	GDP	Population	thinness..1.19.years	thinness.5.9.years	Income.composition.of.resources	Schooling
	Length:2938	Min. :2000	Length:2938	Min. :36.30	Min. : 1.0	Min. : 0.0	Min. : 0.0100	Min. : 0.000	Min. : 1.00	Min. : 0.0	Min. : 1.00	Min. : 0.00	Min. : 3.00	Min. : 0.370	Min. : 2.00	Min. : 0.100	Min. : 1.68	Min. :3.400e+01	Min. : 0.10	Min. : 0.10	Min. :0.0000	Min. : 0.00
	Class :character	1st Qu.:2004	Class :character	1st Qu.:63.10	1st Qu.: 74.0	1st Qu.: 0.0	1st Qu.: 0.8775	1st Qu.: 4.685	1st Qu.:77.00	1st Qu.: 0.0	1st Qu.:19.30	1st Qu.: 0.00	1st Qu.:78.00	1st Qu.: 4.260	1st Qu.:78.00	1st Qu.: 0.100	1st Qu.: 463.94	1st Qu.:1.958e+05	1st Qu.: 1.60	1st Qu.: 1.50	1st Qu.:0.4930	1st Qu.:10.10
	Mode :character	Median :2008	Mode :character	Median :72.10	Median :144.0	Median : 3.0	Median : 3.7550	Median : 64.913	Median :92.00	Median : 17.0	Median :43.50	Median : 4.00	Median :93.00	Median : 5.755	Median :93.00	Median : 0.100	Median : 1766.95	Median :1.387e+06	Median : 3.30	Median : 3.30	Median :0.6770	Median :12.30
	NA	Mean :2008	NA	Mean :69.22	Mean :164.8	Mean : 30.3	Mean : 4.6029	Mean : 738.251	Mean :80.94	Mean : 2419.6	Mean :38.32	Mean : 42.04	Mean :82.55	Mean : 5.938	Mean :82.32	Mean : 1.742	Mean : 7483.16	Mean :1.275e+07	Mean : 4.84	Mean : 4.87	Mean :0.6276	Mean :11.99
	NA	3rd Qu.:2012	NA	3rd Qu.:75.70	3rd Qu.:228.0	3rd Qu.: 22.0	3rd Qu.: 7.7025	3rd Qu.: 441.534	3rd Qu.:97.00	3rd Qu.: 360.2	3rd Qu.:56.20	3rd Qu.: 28.00	3rd Qu.:97.00	3rd Qu.: 7.492	3rd Qu.:97.00	3rd Qu.: 0.800	3rd Qu.: 5910.81	3rd Qu.:7.420e+06	3rd Qu.: 7.20	3rd Qu.: 7.20	3rd Qu.:0.7790	3rd Qu.:14.30
	NA	Max. :2015	NA	Max. :89.00	Max. :723.0	Max. :1800.0	Max. :17.8700	Max. :19479.912	Max. :99.00	Max. :212183.0	Max. :87.30	Max. :2500.00	Max. :99.00	Max. :17.600	Max. :99.00	Max. :50.600	Max. :119172.74	Max. :1.294e+09	Max. :27.70	Max. :28.60	Max. :0.9480	Max. :20.70
	NA	NA	NA	NA’s :10	NA’s :10	NA	NA’s :194	NA	NA’s :553	NA	NA’s :34	NA	NA’s :19	NA’s :226	NA’s :19	NA	NA’s :448	NA’s :652	NA’s :34	NA’s :34	NA’s :167	NA’s :163

Dealing with missing values

As we can see from the summary above, there are some missing values in the dataset. Due to the fact that life.expectancy is the most important attribute for our analysis, we have decided to remove all rows where life.expectancy is NA.

data_new <- data[complete.cases(data[ , 'Life.expectancy']),]

After this operation, we still encounter missing values in the following columns: “Alcohol”, “Hepatitis.B”, “BMI”, “Polio”, “Total.expenditure”, “Diphtheria”, “GDP”, “Population”, “thinness..1.19.years”, “thinness.5.9.years”, “Income.composition.of.resources”, “Schooling”. We will fill these NA values with median for each column.

na_columns <- list("Alcohol", "Hepatitis.B", "BMI", "Polio", "Total.expenditure", "Diphtheria", "GDP", "Population", "thinness..1.19.years", "thinness.5.9.years", "Income.composition.of.resources", "Schooling")

for (col in na_columns){
    m <- median(data_new[ , col], na.rm=TRUE)
    print(col)
    print(m)
    data_new[ , col][is.na(data_new[ , col])] <- m
}

## [1] "Alcohol"
## [1] 3.77
## [1] "Hepatitis.B"
## [1] 92
## [1] "BMI"
## [1] 43.35
## [1] "Polio"
## [1] 93
## [1] "Total.expenditure"
## [1] 5.75
## [1] "Diphtheria"
## [1] 93
## [1] "GDP"
## [1] 1764.974
## [1] "Population"
## [1] 1391757
## [1] "thinness..1.19.years"
## [1] 3.3
## [1] "thinness.5.9.years"
## [1] 3.4
## [1] "Income.composition.of.resources"
## [1] 0.677
## [1] "Schooling"
## [1] 12.3

kable(summary(data_new), "html") %>% kable_styling("striped") %>% scroll_box(width = "100%")

	Country	Year	Status	Life.expectancy	Adult.Mortality	infant.deaths	Alcohol	percentage.expenditure	Hepatitis.B	Measles	BMI	under.five.deaths	Polio	Total.expenditure	Diphtheria	HIV.AIDS	GDP	Population	thinness..1.19.years	thinness.5.9.years	Income.composition.of.resources	Schooling
	Length:2928	Min. :2000	Length:2928	Min. :36.30	Min. : 1.0	Min. : 0.00	Min. : 0.010	Min. : 0.000	Min. : 1.00	Min. : 0.0	Min. : 1.00	Min. : 0.00	Min. : 3.00	Min. : 0.370	Min. : 2.00	Min. : 0.100	Min. : 1.68	Min. :3.400e+01	Min. : 0.100	Min. : 0.100	Min. :0.0000	Min. : 0.00
	Class :character	1st Qu.:2004	Class :character	1st Qu.:63.10	1st Qu.: 74.0	1st Qu.: 0.00	1st Qu.: 1.107	1st Qu.: 4.854	1st Qu.:82.00	1st Qu.: 0.0	1st Qu.:19.40	1st Qu.: 0.00	1st Qu.:78.00	1st Qu.: 4.370	1st Qu.:78.00	1st Qu.: 0.100	1st Qu.: 578.80	1st Qu.:4.181e+05	1st Qu.: 1.600	1st Qu.: 1.600	1st Qu.:0.5040	1st Qu.:10.30
	Mode :character	Median :2008	Mode :character	Median :72.10	Median :144.0	Median : 3.00	Median : 3.770	Median : 65.611	Median :92.00	Median : 17.0	Median :43.35	Median : 4.00	Median :93.00	Median : 5.750	Median :93.00	Median : 0.100	Median : 1764.97	Median :1.392e+06	Median : 3.300	Median : 3.400	Median :0.6770	Median :12.30
	NA	Mean :2008	NA	Mean :69.22	Mean :164.8	Mean : 30.41	Mean : 4.559	Mean : 740.321	Mean :83.05	Mean : 2427.9	Mean :38.29	Mean : 42.18	Mean :82.62	Mean : 5.916	Mean :82.39	Mean : 1.748	Mean : 6627.39	Mean :1.026e+07	Mean : 4.834	Mean : 4.865	Mean :0.6301	Mean :12.02
	NA	3rd Qu.:2011	NA	3rd Qu.:75.70	3rd Qu.:228.0	3rd Qu.: 22.00	3rd Qu.: 7.400	3rd Qu.: 442.614	3rd Qu.:96.00	3rd Qu.: 362.2	3rd Qu.:56.10	3rd Qu.: 28.00	3rd Qu.:97.00	3rd Qu.: 7.330	3rd Qu.:97.00	3rd Qu.: 0.800	3rd Qu.: 4793.63	3rd Qu.:4.593e+06	3rd Qu.: 7.100	3rd Qu.: 7.200	3rd Qu.:0.7730	3rd Qu.:14.10
	NA	Max. :2015	NA	Max. :89.00	Max. :723.0	Max. :1800.00	Max. :17.870	Max. :19479.912	Max. :99.00	Max. :212183.0	Max. :77.60	Max. :2500.00	Max. :99.00	Max. :17.600	Max. :99.00	Max. :50.600	Max. :119172.74	Max. :1.294e+09	Max. :27.700	Max. :28.600	Max. :0.9480	Max. :20.70

As we can see, we have successfully dealt with missing values.

In-depth analysis of attributes (i.e. value distribution)

names(data_new)

##  [1] "Country"                         "Year"                           
##  [3] "Status"                          "Life.expectancy"                
##  [5] "Adult.Mortality"                 "infant.deaths"                  
##  [7] "Alcohol"                         "percentage.expenditure"         
##  [9] "Hepatitis.B"                     "Measles"                        
## [11] "BMI"                             "under.five.deaths"              
## [13] "Polio"                           "Total.expenditure"              
## [15] "Diphtheria"                      "HIV.AIDS"                       
## [17] "GDP"                             "Population"                     
## [19] "thinness..1.19.years"            "thinness.5.9.years"             
## [21] "Income.composition.of.resources" "Schooling"

quantitive_cols = c("Year", "Life.expectancy", "Adult.Mortality", "infant.deaths", "Alcohol", "percentage.expenditure", "Hepatitis.B", "Measles", "BMI", "under.five.deaths", "Polio", "Total.expenditure", "Diphtheria","HIV.AIDS","GDP","Population", "thinness..1.19.years","thinness.5.9.years",     "Income.composition.of.resources", "Schooling")

plots <- lapply(quantitive_cols, function(var) {
  plot_ly(y = data_new[, var], type = "box", name=var, quartilemethod="exclusive")
})
fig <- subplot(plots, nrows=6)
fig <- fig %>% layout(autosize = F, width = 800, height = 500)
fig

plots <- lapply(quantitive_cols, function(var) {
  plot_ly(x = data_new[, var], name=var)%>%
  add_histogram()
})
fig <- subplot(plots, nrows=6)
fig <- fig %>% layout(autosize = F, width = 800, height = 500)

## Warning: Specifying width/height in layout() is now deprecated.
## Please specify in ggplotly() or plot_ly()

fig

p1 <- plot_ly(data_new, x = ~Status) %>%
  add_histogram()

p1

Corelation between variables (graphic presentation)

correlation_data <- data_new[quantitive_cols]

fig <- plot_ly(
    x = quantitive_cols,
    y = quantitive_cols,
    z = cor(correlation_data), type = "heatmap"
)

fig

The above chart gives us important information about the correlation between variables. As we can see, there is almost perfect correlation between thinness.1.19.years and thinness.5.9.years. There also appears to be a very strong correlation between GDP and percentage.expenditure (0.9), as well as infant.deaths and under.five.deaths (0.99). Naturally, we can also see a strong negative correlation between Adult.Mortality and Life.expectancy (-0.69). Schooling and life expectancy seem to be slightly correlated as well (0.71).

For our prediction, we will need to drop some of the features that are highly correlated. We will drop thinness.5.9.years, percentage.expenditure and infant.deaths, as their correlation to our decision variable is weaker than features correlated to them.

Interavtive plot for average life duration per country with respect to year

The following plot is fully interactive - hover over selected line to see a specific value, select one country by double clicking on it in the legend. In one country view, you can then single click on one country to add it to the plot. If you want to return to the view of all countries - double click on the legend again.

countries <- unique(data_new$Country)
fig <- plot_ly(data, x = data_new[data_new$Country == 'Afghanistan', 'Year'])

for(name in countries){
  fig <- fig %>% add_trace(y = data_new[data_new$Country == name, 'Life.expectancy'], name = name, type = 'scatter', mode = 'lines') 
}

fig <- fig %>% layout(legend = list(orientation = 'h'))


fig

Data preparation

regression_data <- data_new[, !names(data_new) %in% c("Country", "thinness.5.9.years", "percentage.expenditure", "infant.deaths", "Year")]


kable(head(regression_data), "html") %>% kable_styling("striped") %>% scroll_box(width = "100%")

Status	Life.expectancy	Adult.Mortality	Alcohol	Hepatitis.B	Measles	BMI	under.five.deaths	Polio	Total.expenditure	Diphtheria	HIV.AIDS	GDP	Population	thinness..1.19.years	Income.composition.of.resources	Schooling
Developing	65.0	263	0.01	65	1154	19.1	83	6	8.16	65	0.1	584.25921	33736494	17.2	0.479	10.1
Developing	59.9	271	0.01	62	492	18.6	86	58	8.18	62	0.1	612.69651	327582	17.5	0.476	10.0
Developing	59.9	268	0.01	64	430	18.1	89	62	8.13	64	0.1	631.74498	31731688	17.7	0.470	9.9
Developing	59.5	272	0.01	67	2787	17.6	93	67	8.52	67	0.1	669.95900	3696958	17.9	0.463	9.8
Developing	59.2	275	0.01	68	3013	17.2	97	68	7.87	68	0.1	63.53723	2978599	18.2	0.454	9.5
Developing	58.8	279	0.01	66	1989	16.7	102	66	9.20	66	0.1	553.32894	2883167	18.4	0.448	9.2

Regressor for average life duration estimation

Train test valid split

trainval_partition <- 
    createDataPartition(
        y = regression_data$Life.expectancy,
        p = .8,
        list = FALSE)

trainval_data <- regression_data[ trainval_partition,]
test_data  <- regression_data[-trainval_partition,]

train_partition <- 
    createDataPartition(
        y = trainval_data$Life.expectancy,
        p = .8,
        list = FALSE)

train_data <- trainval_data[ train_partition,]
val_data  <- trainval_data[-train_partition,]

control <- trainControl(
    method = "repeatedcv",
    number = 10,
    repeats = 5)

linear <- train(Life.expectancy ~ .,
               data = train_data,
               trControl = control,
               preProcess = c('scale', 'center'),
               method = "lm")
linear

## Linear Regression 
## 
## 1878 samples
##   16 predictor
## 
## Pre-processing: scaled (16), centered (16) 
## Resampling: Cross-Validated (10 fold, repeated 5 times) 
## Summary of sample sizes: 1690, 1690, 1690, 1690, 1690, 1690, ... 
## Resampling results:
## 
##   RMSE      Rsquared   MAE     
##   4.232504  0.8022808  3.159272
## 
## Tuning parameter 'intercept' was held constant at a value of TRUE

Model parameter tuning and accuracy calculation using R2 and RMSE measures

lasso <- train(Life.expectancy ~ .,
               data = train_data,
               trControl = control,
               preProcess = c('scale', 'center'),
               method = "lasso")
lasso

## The lasso 
## 
## 1878 samples
##   16 predictor
## 
## Pre-processing: scaled (16), centered (16) 
## Resampling: Cross-Validated (10 fold, repeated 5 times) 
## Summary of sample sizes: 1690, 1690, 1689, 1690, 1688, 1691, ... 
## Resampling results across tuning parameters:
## 
##   fraction  RMSE      Rsquared   MAE     
##   0.1       8.534207  0.6981532  6.941555
##   0.5       5.498991  0.7556058  4.146438
##   0.9       4.251140  0.8009618  3.155516
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.9.

ridge <- train(Life.expectancy ~ .,
               data = train_data,
               trControl = control,
               preProcess = c('scale', 'center'),
               method = "ridge")
ridge

## Ridge Regression 
## 
## 1878 samples
##   16 predictor
## 
## Pre-processing: scaled (16), centered (16) 
## Resampling: Cross-Validated (10 fold, repeated 5 times) 
## Summary of sample sizes: 1689, 1691, 1691, 1689, 1689, 1690, ... 
## Resampling results across tuning parameters:
## 
##   lambda  RMSE      Rsquared   MAE     
##   0e+00   4.228416  0.8031364  3.159813
##   1e-04   4.228416  0.8031369  3.159841
##   1e-01   4.275729  0.8030123  3.230414
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 1e-04.

Attribute importance analysis for the best model found

ggplot(varImp(ridge))

What attribute contributes the most to longer or shorter life duration?